After excluding LD, a total of 13 SNPs exhibited significant correlation with hyperthyroidism, while 75 SNPs showed strong correlation with hypothyroidism. Among them, 12 SNPs were chosen as alternative IVs for conducting MR analysis of hyperthyroidism and RA. Three SNPs associated with the outcome (rs6679677, rs2856821 and rs3087243) were excluded, no confounding SNPs could be detected. Additionally, one palindromic SNP (rs385863) was removed. Consequently, a set of eight SNPs was obtained as IVs for the causal evaluation of hyperthyroidism and RA, as presented in Supplementary Table 2. For the analysis of hypothyroidism and RA, a total of 70 SNPs were selected as alternative IVs. Eight SNPs (rs9271365, rs6679677, rs9277559, rs9264277, rs3087243, rs7574865, rs3184504 and rs34536443) associated with the outcome were excluded, along with one confounding SNPs (rs4409785), and two palindromic SNPs (rs2412976 and rs2921053). In addition, 11 outliers (rs11171710, rs12379417, rs2988277, rs3118469, rs11875260, rs12117927, rs1364450, rs244685, rs7441808, rs2247314 and rs7030280) were removed through MR-PRESSO analysis. Finally, a set of 48 SNPs was obtained as IVs for the causal evaluation of hypothyroidism and RA, as presented in Supplementary Table 3.

The random-effects IVW analysis indicated that there was no genetic causal relationship between hyperthyroidism and RA (P = 0.702, odds ratio [OR] 95% confidence interval [CI] = 1.021 [0.918–1.135]). Similar results were observed across multiple methods, including MR Egger, weighted median, simple mode, and weighted mode, which all failed to establish a genetic causal relationship between hyperthyroidism and RA (P > 0.05) (Figs. 2, 3a and 3b). Notably, both the Cochran’s Q statistic for MR-IVW and Rucker’s Q statistic for MR Egger demonstrated no heterogeneity in the genetic causality assessment between hyperthyroidism and RA (P > 0.05). The intercept test for MR Egger and the MR-PRESSO provided no evidence of horizontal pleiotropy in the genetic causality assessment (P > 0.05). Additionally, the MR-PRESSO indicated the absence of any outlier affecting the genetic causality assessment between hyperthyroidism and RA (Table 1). The “Leave one out” analysis demonstrated that the genetic causality assessment between hyperthyroidism and RA was not influenced by any individual SNPs (Fig. 3c). Furthermore, the MR-RAPS analysis revealed that the genetic causality assessment between hyperthyroidism and RA followed a normal distribution (Table 1; Fig. 3d).

MR analysis results of hyperthyroidism, hypothyroidism and rheumatoid arthritis of test cohort. Five methods: random-effects IVW, MR Egger, weighted median, simple mode, and weighted mode. The primary analysis method used was random-effects IVW. Random-effects IVW is the gold standard of MR analysis, supplemented by MR Egger, weighted median, simple mode, and weighted mode. If the results of the five methods are inconsistent, the random-effects IVW analysis result prevails

MR analysis of hyperthyroidism and rheumatoid arthritis for test cohort. a Scatter plot, the effect of SNPs on hypothyroidism in horizontal coordinate and effect of SNPs on rheumatoid arthritis in vertical coordinate. b The forest map, contains a total of 8 SNPs. Each horizontal line segment represents an SNP effect estimate and its 95% confidence interval. All-MR-Egger represents a comprehensive estimate of the effect size of all SNPs using the MR-Egger method. All-IVW represents a comprehensive estimate of the effect size of all SNPs using the IVW method. c Leave-one-out analysis, delete other SNPs, and use the remaining SNP for MR analysis. All represents an estimate of the total effect size including all SNPs using the IVW method. Each horizontal line represents an estimate of the effect of all SNPs on the result, with the exception of a particular SNP, and its 95% confidence interval. d Normal distribution map, to test whether genetic causality conforms to normal distribution. A total of 8 SNPs were included, and the symmetrical distribution of SNPs on both sides of the oblique line indicated that the genetic causality was normally distributed

The random-effects IVW analysis indicated a positive genetic causal relationship between hypothyroidism and RA (P < 0.001, OR 95% CI = 1.239 [1.140–1.347]). The other four methods do not yield consistent results (Figs. 2, 4a and 4b). No evidence of heterogeneity or horizontal pleiotropy was found (P > 0.05). The 11 outliers were found to be removed during analysis (Table 1). In addition, the “Leave one out” analysis indicated that the genetic causality assessment between hypothyroidism and RA remained consistent even after one remaining SNP (Fig. 4c). The MR-RAPS analysis confirmed that the genetic causality assessment between hypothyroidism and RA followed a normal distribution (P > 0.05) (Table 1; Fig. 4d).

MR analysis of hypothyroidism and rheumatoid arthritis for test cohort. a Scatter plot, the effect of SNPs on hypothyroidism in horizontal coordinate and effect of SNPs on rheumatoid arthritis in vertical coordinate. b The forest map, contains a total of 48 SNPs. Each horizontal line segment represents an SNP effect estimate and its 95% confidence interval. All-MR-Egger represents a comprehensive estimate of the effect size of all SNPs using the MR-Egger method. All-IVW represents a comprehensive estimate of the effect size of all SNPs using the IVW method. c Leave-one-out analysis, delete other SNPs, and use the remaining SNP for MR analysis. All represents an estimate of the total effect size including all SNPs using the IVW method. Each horizontal line represents an estimate of the effect of all SNPs on the result, with the exception of a particular SNP, and its 95% confidence interval. d Normal distribution map, to test whether genetic causality conforms to normal distribution. A total of 48 SNPs were included, and the symmetrical distribution of SNPs on both sides of the oblique line indicated that the genetic causality was normally distributed

After the exclusion of LD, a total of seven SNPs demonstrated significant correlation with hyperthyroidism, while 56 SNPs exhibited strong correlation with hypothyroidism. From this pool, seven SNPs were selected as IVs for the implementation of MR analysis concerning hyperthyroidism and RA. Notably, two SNPs (rs6679677 and rs9271671) associated with the outcome were excluded from the analysis, as no confounding SNPs were eligible for removal. Furthermore, one SNP displaying incompatible alleles (rs9265890) was eliminated. Consequently, a subset of four SNPs was identified as IVs for the causal assessment of hyperthyroidism and RA, delineated in Supplementary Table 4. In the context of the investigation into hypothyroidism and RA, a cohort of 55 SNPs was designated as alternative IVs. Following the exclusion of two SNPs (rs6679677 and rs9273400) linked to the outcome, along with nine confounding SNPs (rs7310615, rs9277542, rs707937, rs10517086, rs11571297, rs11889341, rs244687, rs4409785, rs7902146), and five palindromic SNPs (rs17786733, rs4549506, rs7310615, rs7754251, rs9842232), a set of 40 SNPs was ultimately identified as IVs for the causal evaluation of hypothyroidism and RA, as outlined in Supplementary Table 5.

The random-effects IVW analysis revealed no evidence supporting a genetic causal relationship between hyperthyroidism and RA (P = 0.129, OR 95% CI = 0.999 [0.999–1.000]). This finding was consistent across various analytical methodologies, including MR Egger, weighted median, simple mode, and weighted mode (P > 0.05) (Figs. 5, 6a and 6b). Notably, there exists heterogeneity in the assessment of genetic causality (P < 0.05), albeit without evidence of horizontal pleiotropy (P > 0.05). Furthermore, no outliers were identified (Table 1). The evaluation of genetic causality between hyperthyroidism and RA remained unaffected by any individual SNPs (Fig. 6c). Moreover, the distribution of genetic causality assessment between hyperthyroidism and RA adhered to a normal distribution pattern (Table 1; Fig. 6d). It is important to highlight that due to the constraints of MR-RAPS, which solely provides p-values for MR analyses involving at least seven IVs, the current study, with only four IVs, could not yield a reported p-value by MR-RAPS (Table 1).

MR analysis results of hyperthyroidism, hypothyroidism and rheumatoid arthritis of validation cohort. Five methods: random-effects IVW, MR Egger, weighted median, simple mode, and weighted mode. The primary analysis method used was random-effects IVW. Random-effects IVW is the gold standard of MR analysis, supplemented by MR Egger, weighted median, simple mode, and weighted mode. If the results of the five methods are inconsistent, the random-effects IVW analysis result prevails

MR analysis of hyperthyroidism and rheumatoid arthritis for validation cohort. a Scatter plot, the effect of SNPs on hypothyroidism in horizontal coordinate and effect of SNPs on rheumatoid arthritis in vertical coordinate. b The forest map, contains a total of 4 SNPs. Each horizontal line segment represents an SNP effect estimate and its 95% confidence interval. All-MR-Egger represents a comprehensive estimate of the effect size of all SNPs using the MR-Egger method. All-IVW represents a comprehensive estimate of the effect size of all SNPs using the IVW method. c Leave-one-out analysis, delete other SNPs, and use the remaining SNP for MR analysis. All represents an estimate of the total effect size including all SNPs using the IVW method. Each horizontal line represents an estimate of the effect of all SNPs on the result, with the exception of a particular SNP, and its 95% confidence interval. d Normal distribution map, to test whether genetic causality conforms to normal distribution. A total of 4 SNPs were included, and the symmetrical distribution of SNPs on both sides of the oblique line indicated that the genetic causality was normally distributed

The random-effects IVW analysis revealed a positive genetic causal association between hypothyroidism and RA (P = 0.004, OR 95% CI = 1.001 [1.000–1.001]). Subsequent MR analyses, encompassing MR Egger, weighted median, simple mode, and weighted mode, yielded findings incongruent with the presence of a genetic causal link between hypothyroidism and RA (P > 0.05) (Figs. 5, 7a and 7b). Notably, assessments for heterogeneity, horizontal pleiotropy, and outlier detection did not reveal significant deviations from expected patterns (P > 0.05) (Table 1). Further, the “Leave-one-out” analysis indicated that the inferred genetic causality between hypothyroidism and RA remains robust in the retain of individual SNPs (Fig. 7c). Furthermore, the evaluation of genetic causality adhered to a normal distribution (P > 0.05) (Table 1; Fig. 7d).

MR analysis of hypothyroidism and rheumatoid arthritis for validation cohort. a Scatter plot, the effect of SNPs on hypothyroidism in horizontal coordinate and effect of SNPs on rheumatoid arthritis in vertical coordinate. b The forest map, contains a total of 40 SNPs. Each horizontal line segment represents an SNP effect estimate and its 95% confidence interval. All-MR-Egger represents a comprehensive estimate of the effect size of all SNPs using the MR-Egger method. All-IVW represents a comprehensive estimate of the effect size of all SNPs using the IVW method. c Leave-one-out analysis, delete other SNPs, and use the remaining SNP for MR analysis. All represents an estimate of the total effect size including all SNPs using the IVW method. Each horizontal line represents an estimate of the effect of all SNPs on the result, with the exception of a particular SNP, and its 95% confidence interval. d Normal distribution map, to test whether genetic causality conforms to normal distribution. A total of 40 SNPs were included, and the symmetrical distribution of SNPs on both sides of the oblique line indicated that the genetic causality was normally distributed